The disaggregated integer L-shaped method for the stochastic vehicle routing problem

TL;DR

This paper introduces a novel integer L-shaped method tailored for two-stage stochastic integer programs with decomposable solutions, demonstrating its effectiveness on stochastic vehicle routing problems with demand uncertainties.

Contribution

It develops a new disaggregated L-shaped method with specialized optimality cuts for problems with decomposable solutions, particularly applied to stochastic vehicle routing with demand distributions.

Findings

Achieves state-of-the-art computational results.

Effectively handles stochastic demands with new lower bounds.

Demonstrates the method's applicability to vehicle routing problems.

Abstract

This paper proposes a new integer L-shaped method for solving two-stage stochastic integer programs whose first-stage solutions can decompose into disjoint components, each one having a monotonic recourse function. In a minimization problem, the monotonicity property stipulates that the recourse cost of a component must always be higher or equal to that of any of its subcomponents. The method exploits new types of optimality cuts and lower bounding functionals that are valid under this property. The stochastic vehicle routing problem is particularly well suited to be solved by this approach, as its solutions can be decomposed into a set of routes. We consider the variant with stochastic demands in which the recourse policy consists of performing a return trip to the depot whenever a vehicle does not have sufficient capacity to accommodate a newly realized customer demand. This work shows that this policy can lead to a non-monotonic recourse function, but that the monotonicity holds when the customer demands are modeled by several commonly used families of probability distributions. We also present new problem-specific lower bounds on the recourse that strengthen the lower bounding functionals and significantly speed up the resolution process. Computational experiments on instances from the literature show that the new approach achieves state-of-the-art results.